Factorkappa

Factorkappa is a term found in some mathematical discussions and puzzle literature to denote a factor-related invariant or function associated with a positive integer κ. It is not a standard object in mathematics, and different writers have proposed different definitions, resulting in multiple interpretations.

One common usage defines factorkappa(κ) as the radical of κ, i.e., the product of the distinct prime divisors of κ. For example, κ = 60 has prime divisors 2, 3 and 5, so factorkappa(60) = 2 × 3 × 5 = 30. This interpretation emphasizes the multiplicative skeleton of κ’s prime factorization.

Another frequent definition interprets factorkappa(κ) as the number of unordered factorizations of κ into factors greater than 1. For 60, the unordered two-factor factorizations are (2,30), (3,20), (4,15), (5,12), and (6,10), giving factorkappa(60) = 5 under this convention. Some authors extend the idea to count all factorizations with more than two factors.

In other texts factorkappa is used informally as a placeholder for any standard multiplicative function derived from κ’s divisors, such as the divisor function d(κ). In set theory or abstract algebra contexts, factorkappa may denote a cardinal or invariant related to the structure of κ, with definitions varying by author.

See also rad(n), divisor function, prime factorization, factorization invariants.